In the Bible study I'm involved with we talked about 1 Peter 3:13-16 a few weeks back. I thought these notes might be of interest to some.
In the first section here (verses 13-16) Peter again notes that by doing good Christians will not naturally be the target of persecution. However, Christians may still suffer but will have a clear conscience if they continue to do what is right. Interestingly, although this passage is the root of the branch of Christian study known as apologetics (from apologia, or a “make a defense” in the NASB) note that Peter has in mind here that non-Christians will ask the Christian why their behavior differs from that of the world. From this one can conclude that the primary part of our witness is through our behavior towards others.
That said, some of the various basic “arguments” Christians have used when giving an answer include:
a) Argument from Experience – the personal transformation in the life of a believer as manifested in actions. This to me is what the author of 1 Peter has in mind
b) Argument from Reason – human reason is explainable only through the existence of a creator. I've blogged about this argument in the past as it was used C.S. Lewis in his 1947 book Miracles. Over Christmas I received C.S. Lewis' Dangerous Idea by Reppert, which is both a defense and a refinement of Lewis' argument. Very readable even for those without a philosophical background such as myself.
c) Cosmological Argument – kalam is the most popular form of this argument, originally formulated by Islamic philosophers in the late middle ages, which basically states that whatever had a beginning began to exist at a point in time in the past, and that anything that began to exist had to have a cause. Since the universe began to exist at a finite time in the past (as evidenced by the Big Bang), then it had a beginning and therefore a cause. That cause can reasonably be identified as God.
d) Ontological Argument – developed by St. Anselm and goes like this; God is that which than nothing greater can be conceived. It is better for God to exist than for Him not to exist (an existing object, by definition, is better than non-existence). Therefore, God exists [because it is better for him to exist than not to exist; and if he is "that which than nothing greater can be conceived", he necessarily must exist.] Thus, by considering and examining the following propositions, we must admit that an idea of God necessitates his existence. Thomas Acquinas refined this argument a bit but it has been attacked by modern philosophers and so is not in vogue.
e) Argument from Design – the creation is only explainable as the product of a designer. This argument can take both a cosmological bent (by pointing out the apparent “fine-tuning” of the cosmological constants such as the nuclear forces etc.) or natural bent (natural theology as in the watchmaker arguments of William Paley, 1743-1805). More recently, the Intelligent Design (ID) movement spurred by William Dembski uses this argument in relation to the information content of DNA and the existence of irreducibly complex systems in living beings such as the blood clotting system described by Michael Behe
f) Argument from Joy – a human’s longing for God proves the existence of God just as our longing for food proves that food exists. This argument was used quite effectively by C.S. Lewis
g) Argument from History – two pronged, the NT documents are historically reliable based on documentary evidence and since they are it is logical to believe that Jesus is who he said he was (known as the Trilemma, i.e. Lord, Liar, or Lunatic). This argument was used effectively by Josh McDowell in Evidence That Demands a Verdict.
h) Argument from the Human Condition – Christianity explains human sinfulness combined with a knowledge of that sinfulness and provides a solution
i) Moral Argument – a knowledge of objective moral law or values exist, and a belief in a giver of the moral law best explains its existence. Used by C.S. Lewis in Mere Christianity (“something above and beyond the actual facts of human behaviour. In this case, besides the actual facts, you have something else – a real law which we did not invent and which we know we ought to obey”) and The Abolition of Man as well explained by Moreland and Craig.
 See my blog at http://danagonistes.blogspot.com/2004/11/argument-from-reason.html
 William Lane Craig has a good explanation of the kalam argument in Reasonable Faith. J.P. Moreland has another explanation in Scaling the Secular City.
 An interesting critique of Behe’s book Darwin’s Black Box can be found at http://www.talkorigins.org/faqs/behe.html
 See Surpised by Joy, C.S. Lewis